ACR Y UNAUTH CLB THROUGH ASSIGNED ALT NON ADHERENCE TO ATC CLRNC HAD LTSS FROM ACR X. PLTDEV. POSSIBLE SYS ERROR.

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ACR X WAS CRUISING AT FL310 ON J6 JUST W OF BOWLING GREEN; KY; VOR. JUST AS ZME WAS CALLING OUT TFC NEAR OUR 12 O'CLOCK POS; A TA IMMEDIATELY FOLLOWED BY AN RA TO 'CLB' WAS GIVEN BY TCASII. I IMMEDIATELY INITIATED A CLB AND ADVISED ATC I WAS CLBING TO AVOID A CONFLICT WITH THE OTHER ACFT BUT MY CALL WENT UNACKNOWLEDGED. UPON REACHING 31600 A 'CLR OF CONFLICT' WAS GIVEN AND A DSCNT TO 310 WAS INITIATED. JUST THEN ATC ASKED US WHAT OUR ALT WAS. WE ADVISED THEM WE WERE AT 31600 TO AVOID A CONFLICT BUT WERE NOW DSNDING BACK TO 310. THERE WAS SOME UNCERTAINTY AS TO WHAT ALT THE OTHER ACFT WAS AT. WE ASKED WHAT WAS THE ALT OF THE OTHER ACFT AND ATC SAID THEY WOULD GET BACK TO US BUT THEY NEVER DID. WE WERE SOON HANDED OFF TO THE NEXT CTLR. WE ESTIMATE THE 2 ACFT CAME WITHIN LESS THAN 1000 FT VERTICALLY AND JUST UNDER A MILE OF EACH OTHER. ALSO; THE OTHER ACFT APPEARED TO BE CLBING THROUGH OUR ALT AS IT PASSED IN FRONT OF US. SUPPLEMENTAL INFO FROM ACN 241335: ACR Y WAS OBSERVED CLBING XING PASSING R TO L ON A POSSIBLE COLLISION COURSE. THE INCIDENT (RA) AND ALTDEV WAS RPTED IMMEDIATELY TO ZME. ZME INDICATED THEY WOULD INVESTIGATE AND RPT THE ALT. LATER THEY STATED THEY WERE STILL INVESTIGATING; AND WOULD RPT TO US. NO FURTHER RPTS FOLLOWED.